Problem: The grades on a chemistry midterm at Loyola are normally distributed with $\mu = 77$ and $\sigma = 4.0$. Tiffany earned a $75$ on the exam. Find the z-score for Tiffany's exam grade. Round to two decimal places.
Solution: A z-score is defined as the number of standard deviations a specific point is away from the mean We can calculate the z-score for Tiffany's exam grade by subtracting the mean $(\mu)$ from her grade and then dividing by the standard deviation $(\sigma)$ $ { z = \dfrac{x - {\mu}}{{\sigma}}} $ $ { z = \dfrac{75 - {77}}{{4.0}}} $ ${ z \approx -0.50}$ The z-score is $-0.50$. In other words, Tiffany's score was $0.50$ standard deviations below the mean.